Number of Local Minimums

Number of Local Minimums

Puzzle Prime updated 6 months ago 2 Members · 5 Posts
Puzzles
- probability
Puzzle Prime

Administrator
January 21, 2019 at 12:45 am

100 real random numbers between 0 and 1 are written in a row. What is the expected number of local minima in the row, i.e. numbers which do not stand next to a smaller number?
Vivek

Member
October 21, 2020 at 1:15 am

Using Indicator variables. And the ending point situations have probability of 1/2 to be local minimum and others have 1/6. So, 2*(1/2)+98*(1/6) =52/3 =17.3333 ?
- Puzzle Prime
  
  Administrator
  October 21, 2020 at 3:20 am
  
  Yes, this approach works here too 🙂
- Vivek
  
  Member
  October 21, 2020 at 4:11 am
  
  Oops made a mistake…it is 1/3 right? Not 1/6.
- Puzzle Prime
  
  Administrator
  October 21, 2020 at 6:35 am
  
  Yeah it is, 213 and 312. Sorry didn’t notice 🙂